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Nathan wants to use coordinate geometry to prove that the opposite sides of
a rectangle are congruent. He places parallelogram ABCD in the coordinate
plane so that Ais (0,0), B is (a,0), Cis (a, b), and Dis (0, b).
What formula can he use to determine the distance from point C to point D?

Nathan wants to use coordinate geometry to prove that the opposite sides of a rectangle are congruent He places parallelogram ABCD in the coordinate plane so th class=

Respuesta :

GeorgePP

Answer: C

Step-by-step explanation:

So, first you should draw this rectangle and lable the points accordingly. We can see that the x value of D is 0. That point goes in the bottom left and the A point goes in the top left. You should really draw this while im explaining so it makes more sense.

Now we need to figure out where C and B are. B has a y value of 0, so that means B is in the top right corner. C is in the bottom right.

We have this rectangle labeled now, that was the hard part. We want the distance from C to D. That's essentially Δx, which is (a-0). That just equals a itself. Its either choice A.) or choice C.)

In choice A.), they use 0 - 0 which makes no sense because Δy has no 0 values. We can see our change in y is (b - b). All I did was subtract the two y coords, just like Δx.

Answer C.) fits this perfectly. And I just realized i over complicated this problem. You didnt really have to label these points ABCD. But oh well, I still got the right answer. The 3rd paragraph and on is the only imprtant info

The distance from point C to point D is a units option (C) is correct.

What is a distance formula?

It is defined as the formula for finding the distance between two points. It has given the shortest path distance between two points.

The distance formula can be given as:

[tex]\rm d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

We have:

Parallelogram ABCD in the coordinate plane so that A is (0,0), B is (a,0), C is (a, b), and D is (0, b).

The distance between C to D

[tex]\rm d=\sqrt{(0-a)^2+(b-b)^2}[/tex]

[tex]\rm d=\sqrt{(a)^2}[/tex]

d  = a units

Thus, the distance from point C to point D is a units option (C) is correct.

Learn more about the distance formula here:

brainly.com/question/18296211

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